Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 009, 8 pages      arXiv:1001.3656      http://dx.doi.org/10.3842/SIGMA.2010.009
Contribution to the Proceedings of the 5-th Microconference Analytic and Algebraic Methods V

PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues

Emanuela Caliceti a, Francesco Cannata b and Sandro Graffi a
a) Dipartimento di Matematica, Università di Bologna, and INFN, Bologna, Italy
b) INFN, Via Irnerio 46, 40126 Bologna, Italy

Received November 03, 2009, in final form January 14, 2010; Published online January 20, 2010

Abstract
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one-dimensional x2(ix)ε for −1<ε<0.

Key words: PT symmetry; real spectra; perturbation theory.

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